The separated variable in the direction of propagation from the electric and magnetic vector potentials can be defined as a wave incident on a port and a wave reflected from a port,
\begin{align}
V(\rho) &= V^+(\rho) + V^-(\rho)\\
I(\rho) &= I^+(\rho) + I^-(\rho)
\end{align}
These variables are normalized with respect to the wave impedance as follows,
\begin{align}
v(\rho) &= \frac{1}{\sqrt{Z_w}}V(\rho)\\
i(\rho) &= \sqrt{Z_w}I(\rho)
\end{align}
The normalized variables $v(\rho)$ and $i(\rho)$ are then defined in terms of an incident wave ($a$) and a reflected wave ($b$) along with propagation functions that describe how the wave propagates for a given geometry and coordinate system and in which direction the wave is propagating.
\begin{align}
v(\rho) &= a\;v^+(\rho)+b\;v^-(\rho)\\
i(\rho) &= a\;i^+(\rho)+b\;i^-(\rho)
\end{align}
This can be cast into a matrix form as,
\begin{align}
\left[ \begin{array}{c}
v(\rho) \\
i(\rho)
\end{array}\right] = 
\left[ \begin{array}{cc}
v^+(\rho) & v^-(\rho) \\
i^+(\rho) & i^-(\rho)
\end{array} \right]
\left[ \begin{array}{c}
a \\
b
\end{array}\right]
\end{align}
The matrix relates how the total fields are related to the traveling waves.  This matrix describes how the waves propagate and the direction of propagation and therefore will be called the \emph{wave propagation matrix}.  For example, for a uniform cross section waveguide the functions in the matrix would best be described as exponentials (i.e. $\exp(j\beta z)$ with $i_1^- = i_2^+=-1$).  For a non-uniform waveguide cross section such as a radial waveguide whose propagation direction is in the $\rho$ direction the functions would best be described as Hankel functions.  For a spherical cross section spherical Bessel functions should be used, etc.  Note that there is a relationship between $v(\rho)$ and $i(\rho)$ in which one is usually the derivative of the other.